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Unformatted text preview: Hypothesis testing Terminology
• Null hypothesis – e.g. H0: µ = 1 0 , H0: p = .5 , H0: µ1 = µ2 • Alternative hypothesis – e.g. H1 : µ ≠ 1 0 , H1: p < .5 , H1 : µ1 > µ2 •
•
•
•
•
• Type I error?
Type II error?
Significance Level?
Critical Region?
pvalue?
Power?
2 Type I and II errors
• Type I error
– Reject H0 when H0 is true • Type II error
– Accept H0 when H0 is false • Probabilities of Type I and II errors should
be as small as possible
– Fixed sample size
• reducing probability of type I error >increases
probability of type II error
3 Hypothesis testing approach – significance
level
• FIX the maximum allowable probability
of Type I error = α, significance level of
the test
• Test is then arranged to minimize Type
II error
• Most expensive error should represent
Type I error
• Type I error can be fixed
• Under more control than type II error
4 Hypothesis testing example
• Large sample size σ
x ~ N (µ , )
n
2 • One sided test
– H0:µ = µ0 vs H1:µ > µ0 – e.g. H0:µ = 1 0 vs H1:µ > 1 0 Ｉ Ｉ Ｉ Ｉ Ｉ Ｉ is true σ2
n α µ0
Critical region: Reject
H0 µ0 + k x Hypothesis testing approach – significance
level
• FIX the maximum allowable probability
of Type I error = α, significance level of
the test
• Reject H0 if test statistic lies in the
critical region
x − µ0
> zα
1
σ
n
7 Computer Output (pvalue)
• pvalue is a measure of exactly where the
teststatistic lies in the critical region
– Smaller pvalue > more significant result • Reject H0 if pvalue is less than α pvalue measures
how significant a
result is pvalue µ0 x Hypothesis testing approach – power
• Standard tests are designed to
minimize
probability of Type II error = β • Power of the test = 1 – β
• Standard test designed to have
maximum possible power (depending
on effect size)
• Recommended power ∼ 0.8
• Fixed n  increase power by relaxing α?
•
10 ...
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 Spring '09
 ValerieOzaki

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